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| {{lowercase|title=dc (Unix)}}
| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
| '''dc''' is a [[cross-platform]] [[reverse Polish notation|reverse-polish]] '''d'''esk '''c'''alculator which supports [[arbitrary-precision arithmetic]].<ref>{{man|1|dc||an arbitrary precision calculator}}</ref> It is one of the oldest [[Unix]] utilities, predating even the invention of the [[C (programming language)|C programming language]]; like other utilities of that vintage, it has a powerful set of features but an extremely terse syntax.<ref>{{cite web
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| |url=http://plan9.bell-labs.com/7thEdMan/vol2/dc
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| |title=The sources for the manual page for 7th Edition Unix dc
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| }}</ref><ref>{{cite web
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| |author=Ritchie, Dennis M.
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| |date=Sep. 1979
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| |url=http://cm.bell-labs.com/cm/cs/who/dmr/hist.html
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| |title=The Evolution of the Unix Timesharing System
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| }}</ref>
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| Traditionally, the more user-friendly (with its [[infix notation]]) [[bc programming language|bc]] calculator program was implemented on top of dc, although more modern implementations are related in the opposite fashion: dc uses bc's library for arithmetic.<ref>{{cite web
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| |url= http://directory.fsf.org/project/bc/
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| |title=Free Software Directory: BC
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| |accessdate=5 Jan 2009
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| }}</ref>
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| This article provides some examples in an attempt to give a general flavour of the language; for a complete list of commands and syntax, one should consult the [[man page]] for one's specific implementation.
| | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
| | * Only registered users will be able to execute this rendering mode. |
| | * Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere. |
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| ==Basic operations==
| | Registered users will be able to choose between the following three rendering modes: |
| To multiply four and five in dc (note that most of the whitespace is optional):
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| 4 5 *
| | '''MathML''' |
| p
| | :<math forcemathmode="mathml">E=mc^2</math> |
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| This translates into "push four and five onto the stack, then, with the multiplication operator, pop two elements from the stack, multiply them and push the result back on the stack." Then the 'p' command is used to examine (print out to the screen) the top element on the stack.
| | <!--'''PNG''' (currently default in production) |
| | :<math forcemathmode="png">E=mc^2</math> |
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| The [[arithmetic precision]] is changed with the command 'k', which sets the number of fractional digits (the number of digits following the [[radix point|point]]) to be used for arithmetic operations. Since the default precision is zero, this sequence of commands produces '0' as a result:
| | '''source''' |
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| | :<math forcemathmode="source">E=mc^2</math> --> |
| 2 3 / p
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| By adjusting the precision with 'k', arbitrary number of decimal places can be produced. This command sequence outputs '.66666'.
| | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| 5 k
| | ==Demos== |
| 2 3 / p
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| To evaluate <math>\sqrt{(12 + (-3)^4)\over11}-22</math>: ('v' computes the square root of the top of the stack and '_' is used to input a negative number):
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
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| 12 _3 4 ^ + 11 / v 22 -
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| p
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| To swap the top two elements of the stack, use the 'r' command. To duplicate the top element, use the 'd' command.
| | * accessibility: |
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
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| ==Input/Output== | | ==Test pages == |
| To read a line from [[stdin]], use the '?' command. This will evaluate the line as if it were a ''dc'' command, and so it is necessary that it be syntactically correct and potentially be a security problem since the '!' ''dc'' command will allow arbitrary command execution.
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| As mentioned above, 'p' will print the top of the stack with a newline after it. 'n' will pop the top of the stack and output it without a trailing newline. 'f' will dump the entire stack with one entry per line.
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| | *[[Displaystyle]] |
| | *[[MathAxisAlignment]] |
| | *[[Styling]] |
| | *[[Linebreaking]] |
| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
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| ''dc'' also support arbitrary input and output [[radix|radices]]. The 'i' command will pop the top of the stack and use it for the input base. Hex digits must be in upper case to avoid collisions with ''dc'' commands and are not limited to A-F if the input radix is larger than 16. The 'o' command does the same for the output base, but keep in mind that the input base will affect the parsing of every numeric value afterwards so it is usually advisable to set the output base first. To read the values, the 'K', 'I' and 'O' will push the current precision, input radix and output radix on to the top of the stack.
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| | | *[[Url2Image|Url2Image (private Wikis only)]] |
| As an example, to convert from hex to binary:
| | ==Bug reporting== |
| | | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| 16i2o DEADBEEFp
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| outputs <tt>11011110101011011011111011101111</tt>.
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| ==Language Features==
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| ===Registers===
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| In addition to these basic arithmetic and stack operations, dc includes support for [[Macro (computer science)|macros]], conditionals and storing of results for later retrieval.
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| The mechanism underlying macros and conditionals is the '''register''', which in dc is a storage location with a single character name which can be stored to and retrieved from: 'sc' pops the top of the stack and stores it in register c, and 'lc' pushes the value of register c onto the stack. For example:
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| 3 sc 4 lc * p
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| Registers can also be treated as secondary stacks, so values can be pushed and popped between them and the main stack using the 'S' and 'L' commands.
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| ===Strings===
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| String values are enclosed in '[' and ']' characters and may be pushed on the stack and stored in registers. The 'a' command will convert a the low order byte of the numeric value into an [[ASCII#ASCII_printable_characters|ASCII]] character, or if the top of the stack is a string it will replace it with the first character of the string. There are no ways to build up strings or perform string manipulation other than executing it with the 'x' command, or printing it with the 'P' command.
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| The '#' character begins a comment to the end of the line.
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| ===Macros===
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| Macros are then implemented by allowing registers and stack entries to be strings as well as numbers. A string can be printed, but it can also be executed (i.e. processed as a sequence of dc commands). So for instance we can store a macro to add one and then multiply by 2 into register m:
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| [1 + 2 *] sm
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| and then (using the 'x' command which executes the top of the stack) we can use it like this:
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| 3 lm x p
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| ===Conditionals===
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| Finally, we can use this macro mechanism to provide conditionals. The command '=r' will pop two values from the stack, and execute the macro stored in register 'r' only if they are equal. So this will print the string 'equal' only if the top of the stack is equal to 5:
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| <pre>
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| [[equal]p] sm 5 =m
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| </pre>
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| Other conditionals are '>', '!>', '<', '!<', '!=', which will execute the specified macro if the top two values on the stack are greater, less than or equal to ("not greater"), less than, greater than or equal to ("not less than"), and not equals, respectively.
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| ===Loops===
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| Looping is then possible by defining a macro which (conditionally) reinvokes itself. A simple factorial of the top of the stack might be implemented as:
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| # F(x): return x!
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| # if x-1 > 1
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| # return x * F(x-1)
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| # otherwise
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| # return x
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| [d1-d1<F*]dsFxp
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| The '1Q' command will exit from a macro, allowing an early return. 'q' will quit from two levels of macros (and ''dc'' itself if there are less than two levels on the call stack). 'z' will push the current stack depth before the 'z' operation.
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| ==Examples==
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| As an example of a relatively simple program in dc, this command (in 1 line):
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| dc -e <nowiki>'[[Enter a number (metres), or 0 to exit]psj]sh[q]sz[lhx?d0=z10k39.370079*.5+0k12~1/rn[ feet ]
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| Pn[ inches]P10Pdx]dx'</nowiki>
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| will convert distances from metres to feet and inches; the bulk of it is concerned with prompting for input, printing output in a suitable format and looping round to convert another number.
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| As an example, here is an implementation of the [[Euclidean algorithm]] to find the [[Greatest common divisor|GCD]]:
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| dc -e <nowiki>'??[dSarLa%d0<a]dsax+p' # shortest
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| dc -e '[a=]P?[b=]P?[dSarLa%d0<a]dsax+[GCD:]Pp' # easier-to-read version</nowiki>
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| Computing the [[factorial]] of an input value, <math>n! = \prod_{i=1}^n i</math>
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| <pre>
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| dc -e '?[q]sQ[d1=Qd1-lFx*]dsFxp'
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| </pre>
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| A more complex example performs [[Diffie-Hellman key exchange]]. This was popular as a [[signature block]] among [[cypherpunk]]s during the [[ITAR]] debates<ref>{{cite web
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| |url=http://www.cypherspace.org/adam/rsa/perl-dh.html
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| |title=Diffie-Hellman in 2 lines of Perl
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| |accessdate=5 Jan 2009
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| |author=Adam Back
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| }}</ref>:
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| <pre>
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| #!/usr/bin/perl -- -export-a-crypto-system-sig Diffie-Hellman-2-lines
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| ($g,$e,$m)=@ARGV,$m||die"$0 gen exp mod\n";print`echo "16dio1[d2%Sa2/d0<X+d
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| *La1=z\U$m%0]SX$e"[$g*]\EszlXx+p|dc`
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| </pre>
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| A commented version is slightly easier to understand and shows how to use loops, conditionals, and the 'q' command to return from a macro. With a modern version of dc, the '|' command can be used to do arbitrary precision modular exponentiation without needing to write the X function.
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| <source lang=perl>
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| #!/usr/bin/perl
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| my ($g,$e,$m) = map { "\U$_" } @ARGV;
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| die "$0 gen exp mod\n" unless $m;
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| print `echo $g $e $m | dc -e '
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| # Hex input and output
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| 16dio
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| # Read m, e and g from stdin on one line
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| ?SmSeSg
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| # Function z: return g * top of stack
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| [lg*]sz
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| # Function Q: remove the top of the stack and return 1
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| [sb1q]sQ
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| # Function X(e): recursively compute g^e % m
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| # It is the same as Sm^Lm%, but handles arbitrarily large exponents.
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| # Stack at entry: e
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| # Stack at exit: g^e % m
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| # Since e may be very large, this uses the property that g^e % m ==
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| # if( e == 0 )
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| # return 1
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| # x = (g^(e/2)) ^ 2
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| # if( e % 2 == 1 )
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| # x *= g
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| # return x %
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| [
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| d 0=Q # return 1 if e==0 (otherwise, stack: e)
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| d 2% Sa # Store e%2 in a (stack: e)
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| 2/ # compute e/2
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| lXx # call X(e/2)
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| d* # compute X(e/2)^2
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| La1=z # multiply by g if e%2==1
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| lm % # compute (g^e) % m
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| ] SX
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| le # Load e from the register
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| lXx # compute g^e % m
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| p # Print the result
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| '`;
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| </source>
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| == See also ==
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| * [[bc programming language]]
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| * [[Calculator input methods]]
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| * [[HP calculators]]
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| * [[Orpie]], an RPN calculator
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| * [[Stack machine]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| *Package [http://packages.debian.org/search?keywords=dc&searchon=names&exact=1&suite=all§ion=all dc] in [[Debian GNU/Linux]] repositories
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| *[http://gnuwin32.sourceforge.net/packages/bc.htm Native Windows port] of ''[[bc programming language|bc]]'', which includes ''dc''.
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| {{unix commands}}
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| [[Category:cross-platform software]]
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| [[Category:Unix software]]
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| [[Category:free mathematics software]]
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| [[Category:Numerical programming languages]]
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| [[Category:stack-oriented programming languages]]
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| [[cs:Dc (programovací jazyk)]]
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| [[de:Dc (Unix)]]
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| [[fr:Dc (logiciel)]]
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| [[pl:Dc (informatyka)]]
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| [[ru:Dc]]
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| [[es:DC (Unix)]]
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